Computation Methods in Statistical and Quantum Mechanics

研究统计力学和量子凝聚态物理相关领域的计算方法和算法的发展和应用。这些方法的发展主要是计算亚显性转移矩阵特征值和激发态能量，其中主要应用将是(i)临界现象和量子自旋链中的通用振幅；（ii）随机动力学松弛时间谱；（iii）蒙特卡罗误差分析模型；（iv） Lennard-Jones玻色子簇的激发态性质。另一个主题是相对于表面波动（几何和其他）的普适性的振幅表征湿层在体临界。最后，我们提出了一个系统改进的近似方案，用于计算量子链的有限温度热力学。将进行理论和计算研究，以改进用于处理大量粒子相互作用的计算技术。将研究许多不同的系统，以展示所开发的技术。这个项目的成功完成将提供适用于各种重要的计算密集型问题的技术。

Research will be conducted on the development and application of computational methods and algorithms in statistical mechanics and related areas in quantum condensed matter physics. The development of methods predominantly features computation of subdominant transfer matrix eigenvalues and excited state energies, where the main applications will be (i) universal amplitudes in critical phemonena and quantum spin chains; (ii) the relaxation time spectrum of stochastic dynamics; (iii) models for Monte Carlo error analysis; and, (iv) excited state properties of Lennard-Jones boson clusters. Another topic is the universality with respect to surface fluctuations (geometric and other) of amplitudes characterizing wetting layers at bulk criticality. Lastly, we propose to develop a systematically improvable approximation scheme for the computation of the finite temperature thermodynamics of quantum chains. %%% Theoretical and computational research will be done to improve computational techniques used in dealing with the interactions of large numbers of particles. A number of different systems will be studied to demonstrate the developed techniques. The successful completion of this project will provide techniques which are applicible to a variety of important computationally intensive problems.